4n^2-114=5n

Solution for 4n^2-114=5n equation:

4n^2-114=5n

We move all terms to the left:

4n^2-114-(5n)=0

a = 4; b = -5; c = -114;
Δ = b2-4ac
Δ = -52-4·4·(-114)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-43}{2*4}=\frac{-38}{8}
=-4+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+43}{2*4}=\frac{48}{8}
=6
$